The multi-pass nanometric machining of copper with diamond tool was carried out using the Molecular Dynamics (MD) simulation. The copper-copper interactions were modelled by the EAM potential and the copper-diamond interactions were modelled by the Morse potential. The diamond tool was modelled as a deformable body and the Tersoff potential was applied for the carbon-carbon interactions. It was observed that the average tangential and the normal components of the cutting forces reduced in the consecutive cutting passes. Also, the lateral force components are affected by atomic vibrations and the cross sectional area during the cutting process.